Programming Language Foundations is a concise text that covers a wide range of topics in the mathematical semantics of programming languages, for readers without prior advanced background in programming languages theory. The goal of the book is to provide rigorous but accessible coverage of essential topics in the theory of programming languages. Stumps Programming Language Foundations is intended primarily for a graduate-level course in programming languages theory which is standard in graduate-level CS curricula. It may also be used in undergraduate programming theory courses but ONLY where students have a strong mathematical preparation.